A few works have also been devoted to two- or three-dimensional systems (see, e.g., [1]}, [2]}, [3]}). We would like to mention, in particular, the work of Cannata, Ioffe, and Nishnianidze, who studied non-Hermitian two-dimensional systems with either a quadratic interaction [4]} or an anharmonic oscillator one [5]}. Such systems were shown to be nonseparable and nondiagonalizable, although exactly solvable due to their property of shape invariance [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. A generalization to a three-dimensional system with quadratic interaction was also later on studied [12]}.
